Salazar Domingos S P, Lira Sérgio A
Unidade Acadêmica de Educacão a Distância e Tecnologia, Universidade Federal Rural de Pernambuco, Recife, Pernambuco 52171-900 Brazil.
Instituto de Física, Universidade Federal de Alagoas, Maceió, Alagoas 57072-900 Brazil.
Phys Rev E. 2019 Jun;99(6-1):062119. doi: 10.1103/PhysRevE.99.062119.
We perform an analytic study on the stochastic thermodynamics of a small classical particle trapped in a time-dependent single-well potential in the highly underdamped limit. It is shown that the nonequilibrium probability density function for the system's energy is a Maxwell-Boltzmann distribution (as in equilibrium) with a closed form time-dependent effective temperature and fractional degrees of freedom. We also find that the solvable model satisfies the Crooks fluctuation theorem, as expected. Moreover, we compute the average work in this isothermal process and characterize analytically the optimal protocol for minimum work. The optimal protocol presents an initial and a final jump which correspond to adiabatic processes linked by a smooth exponential time-dependent part for all kinds of single-well potentials. Furthermore, we argue that this result connects two distinct relevant experimental setups for trapped nanoparticles, the levitated particle in a harmonic trap, and the free particle in a box, as they are limiting cases of the general single-well potential and display the time-dependent optimal protocols. Finally, we highlight the connection between our system and an equivalent model of a gas of Brownian particles.
我们对处于高度欠阻尼极限下、被困于随时间变化的单阱势中的小经典粒子的随机热力学进行了分析研究。结果表明，系统能量的非平衡概率密度函数是麦克斯韦 - 玻尔兹曼分布（如同在平衡态一样），具有封闭形式的随时间变化的有效温度和分数自由度。我们还发现，这个可解模型如预期那样满足克鲁克斯涨落定理。此外，我们计算了该等温过程中的平均功，并解析地刻画了最小功的最优协议。最优协议呈现出一个初始跳跃和一个最终跳跃，对于所有类型的单阱势，它们对应于由一个平滑的指数时间依赖部分连接的绝热过程。此外，我们认为这个结果将捕获纳米粒子的两种不同的相关实验设置联系起来，即谐波阱中的悬浮粒子和盒子中的自由粒子，因为它们是一般单阱势的极限情况，并展示了随时间变化的最优协议。最后，我们强调了我们的系统与布朗粒子气体的等效模型之间的联系。
